Sampling and estimation of spatial fields using sensors which are location unaware is an exciting
topic. Here we study this topic under the assumption that the sensors are deployed according
to a known probability distribution, under different scenarios.
The initial part of this work studies detection of bandlimited fields from location-unaware
sensors that are restricted to a discrete grid. Oversampling is used to overcome the lack of
location information. The samples obtained from location-unaware sensors are clustered together
to infer the field using the probability distribution that governs sensor placement on the grid.
Based on this clustering algorithm, the main result of this part is to find the optimal probability
distribution on sensor locations that minimizes the detection error-probability of the underlying
spatial field. The proposed clustering algorithm is also extended to include the case of signal
reconstruction in the presence of sensor noise by treating the distribution of the noisy samples
as a mixture model and using clustering to estimate the mixture model parameters.
In the later part of the work the restriction that sensor locations must lie on a discrete grid
is removed. It is already known that location-unaware sensors deployed according to a uniform
distribution cannot infer the field uniquely in the absence of order information on the sensor
locations. We strengthen this result further and give a procedure for estimating the ordering of
sensor locations which is absent in related work. It is also shown that even in the case where
sensors are deployed according to a general (not necessarily uniform) distribution there exist
several fields that cannot be inferred uniquely. This reinforces the need for restricting the sensor
locations to a discrete grid or knowing the ordering on the sensor locations. These are the main
results for this part of the work.